The figure consists of a rectangular prism with dimensions 3x, 2x, and x, and a pyramid on top with a height of x.
The volume of the rectangular prism is given by:
Volume = length x width x height = 3x * 2x * x = 6x^2
The volume of the pyramid is given by:
Volume = 1/3 * base area * height = 1/3 * (3x * 2x) * x = 2x^2
Total volume = Volume of prism + Volume of pyramid
315 = 6x^2 + 2x^2
315 = 8x^2
x^2 = 315 / 8
x^2 = 39.375
x = sqrt(39.375)
x ≈ 6.27
Therefore, the value of x is approximately 6.27.
Use the diagram to solve for the value of x given that the volume of the figure is 315 in3.
1 answer